Multiple solutions of problems with nonlinear first-order differential operators (Q497962)

The paper gives existence and multiplicity results for first order differential equations of the form \[ (\phi(u(t)))'=f(t,u(t))\text{ a.e. }t\in[0,T] \] subject to the periodic condition \(u\left( 0\right) =u\left( T\right) \) or to the initial value condition \(u\left( 0\right) =r\). For these equations, \(\phi :]a,b[\rightarrow \mathbb{R}\) is an increasing homeomorphism and \(f:\left[ 0,T\right] \times \mathbb{R} \rightarrow \mathbb{R}\) is a Carathéodory function. The results are based on techniques of upper and lower solutions and fixed point index theory.